Uncertainty Quantification for Approximate p-Quantiles for Physical Models with Stochastic Inputs
Journal article, 2014

We consider the problem of estimating the p-quantile for a given functional evaluated on solutions of a deterministic model in which model input is subject to stochastic variation. We derive upper and lower bounding estimators of the p-quantile. We perform an a posteriori error analysis for the p-quantile estimators that takes into account the effects of both the stochastic sampling error and the deterministic numerical solution error and yields a computational error bound for the estimators. We also analyze the asymptotic convergence properties of the p-quantile estimator bounds in the limit of large sample size and decreasing numerical error and describe algorithms for computing an estimator of the p-quantile with a desired accuracy in a computationally efficient fashion. One algorithm exploits the fact that the accuracy of only a subset of sample values significantly affects the accuracy of a p-quantile estimator resulting in a significant gain in computational efficiency. We conclude with a number of numerical examples, including an application to Darcy flow in porous media.

Author

Daniel Elfverson

Donald J. Estep

F. Hellman

Axel Målqvist

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION

2166-2525 (ISSN)

Vol. 2 1 826-850

Subject Categories

Mathematics

DOI

10.1137/140967039

More information

Created

12/4/2017